1. Field of the Invention
The present invention relates generally to a Multi-Carrier Modulation (MCM) communication system, and in particular, to an apparatus and method for reducing Peak-to-Average Power Ratio (PAPR) in an Orthogonal Frequency Division Multiplexing (OFDM) system.
2. Description of the Related Art
OFDM is a special case of MCM, in which a serial symbol sequence is, prior to transmission, converted to parallel symbol sequences and modulated to mutually orthogonal sub-carriers.
The first MCM systems appeared in the late 1950's for military High Frequency (HF) radio communications, and OFDM with overlapping orthogonal sub-carriers was initially developed in the 1970's. In view of difficulty in maintaining orthogonal modulation between multiple carriers, OFDM has limitations in applications to real systems. However, in 1971, Weinstein, et al. proposed an OFDM scheme that applies Discrete Fourier Transform (DFT) to parallel data transmission as an efficient modulation/demodulation process, which was a driving force behind the development of OFDM. Also, the introduction of a guard interval and a cyclic prefix as the guard interval further mitigated adverse effects of multi-path propagation and delay spread on systems.
Accordingly, OFDM has been exploited in a wide variety of fields of digital data communications such as Digital Audio Broadcasting (DAB), digital television broadcasting, Wireless Local Area Network (WLAN), and Wireless Asynchronous Transfer Mode (WATM).
OFDM, similar to traditional Frequency Division Multiplexing (FDM), boasts of optimum transmission efficiency in high-speed data transmission because first of all, it transmits data on sub-carriers, maintaining orthogonality among them. Overlapping frequency spectrums leads to efficient frequency and robustness against multi-path fading.
Despite the above-described benefits, OFDM has the distinctive drawback that MCM causes a high PAPR. Since data is transmitted on multiple subcarriers, the amplitude of a final OFDM signal is the sum of the amplitudes of individual subcarriers and thus fluctuates significantly. Moreover, if the subcarriers are in phase, this results in a very high amplitude fluctuation. As a consequence, the signal is out of the linear operation range of a high power amplifier in a Radio Frequency (RF) processor, and after passing through the high power amplifier, signal distortion is produced. In this context, many techniques have been proposed for PAPR reduction.
Traditionally, there are two main kinds of PAPR reduction methods: transparent methods and side information methods. In the transparent methods, a transmitter reduces PAPR and a receiver recovers a signal transmitted by the transmitter without any associated information. In the side information methods, the receiver recovers the transmitted signal using side information existing in the received signal. The transparent methods can be implemented in compliance with existing standards, including clipping and filtering, and peak windowing. The side information methods require standardization before the system is designed. Coding, Selective Mapping (SLM), and Partial Transmit Sequence (PTS) are side information methods.
Clipping and Filtering: The parts of a baseband signal which have magnitudes above a threshold are mapped to a predetermined value or clipped, while the parts of the baseband signal with magnitudes at or below the threshold are passed through the filtering and clipping. After the resulting signal is made smooth by filtering, it is input to an amplifier. This approach is very simple in terms of system implementation, but despite the use of a filter, hard clipping-caused distortion of frequency spectrum interferes with an adjacent frequency band. Moreover, the clipped signal increases the PAPR during the filtering process.
Peak Windowing: The parts of a baseband signal whose magnitudes below a threshold are multiplied by ‘1’ and thus transmitted as the original signal, while predetermined impulses are created for the parts of the baseband signal with magnitudes at or above the threshold, a convolution of the impulses and a window is subtracted from ‘1’, and then the resulting signal is multiplied by the original signal, thereby limiting peaks to or below a predetermined threshold. This technique does not need side information and has good frequency spectrum when the window size increases. However, when peaks exceeding the threshold successively exist at smaller intervals than the window size W, the amplitude of the original signal is over-limited and thus average Bit Error Rate (BER) is increased during the period of the original signal.
SLM: Data of N OFDM symbol periods is multiplied by statistically independent M pairs of sequences (length N) and Inverse-Fast-Fourier-Transform (IFFT)-processed. The PAPRs of the IFFT signals are calculated and data is transmitted using a sequence with the lowest PAPR. Information about the sequence is also transmitted as side information. Due to the IFFT process, transmitter complexity increases by almost a factor of M and the transmission of side information is rather constraining.
PTS: Like SLM, PTS relies on the linearity of IFFT. A frequency-domain input signal is divided into M subblocks and N-point IFFT-processed. Each subblock is multiplied by a phase factor so that its PAPR is minimized and then the subblocks are summed. Since M IFFTs are required and the computation volume of calculating phase factors significantly increases with the number of subblocks, high-speed information transmission cannot be achieved. In addition, side information must be transmitted as in SLM.
Among the above techniques, peak windowing will be described in more detail.
Peak windowing is one of techniques proposed to improve spectrum distortion caused by clipping. In the clipping technique for limiting the amplitude of an input signal to a high-power amplifier, hard clipping of a particular amplitude area degrades out-of-band radiation characteristics in the frequency spectrum. The out-of-band radiation characteristics are improved by windowing the clipped area and thus smoothing a time-domain signal in the peak windowing technique, as illustrated in FIG. 1. In the conventional peak windowing, the amplitude of a clipped signal is expressed as Equation (1):
                                                                                    x                s                            ⁡                              (                n                )                                                          =                                    c              ⁡                              (                n                )                                      ·                                                        x                ⁡                                  (                  n                  )                                                                                  ⁢                                  ⁢                              c            (            n            ⁢                                                  )                    =                      {                                                                                1                    ,                                                                                                                                                            x                        ⁡                                                  (                          n                          )                                                                                                            ≤                    A                                                                                                                                          A                                                                                                x                          n                                                                                                              ,                                                                                                                                                            x                        ⁡                                                  (                          n                          )                                                                                                            >                    A                                                                                                          (        1        )            where n is a sample index of a discrete signal, x(n) is a baseband signal after IFFT, xs(n) is a clipped signal, A is a threshold for clipping, and c(n) is a scaling factor for PAPR reduction.
The scaling factor is given by Equation (2):
                                          s            ⁡                          (              n              )                                =                      1            -                                          ∑                                  k                  =                  –∞                                ∞                            ⁢                                                a                  ⁡                                      (                    k                    )                                                  ⁢                                  w                  ⁡                                      (                                          n                      -                      k                                        )                                                                                      ⁢                                  ⁢                                                                              a                  ⁡                                      (                    k                    )                                                  =                                  1                  -                                      c                    ⁡                                          (                      k                      )                                                                                                                                              =                                  {                                                                                                              0                          ,                                                                                                                                                                                                            x                              ⁡                                                              (                                n                                )                                                                                                                                          ⁢                                                                                                          ≤                                                                                                          ⁢                          A                                                                                                                                                                                          1                            -                                                          A                                                                                                                                x                                  ⁡                                                                      (                                    n                                    )                                                                                                                                                                                                                ,                                                                                                                                                                                                            x                              ⁡                                                              (                                n                                )                                                                                                                                          ⁢                                                                                                          >                                                                                                          ⁢                          A                                                                                                                                                                            (        2        )            where s(n) is the scaling factor, w(n) is a window function (e.g. Hamming, Hanning, and Kaiser windows), and a(k) is a weighting coefficient. s(n) can be simplified to Equation (3):
                              s          ⁡                      (            n            )                          =                  1          -                                    ∑                              k                =                                  -                  ∞                                            ∞                        ⁢                                          [                                  1                  -                                      c                    ⁡                                          (                      k                      )                                                                      ]                            ⁢                              w                ⁡                                  (                                      n                    -                    k                                    )                                                                                        (        3        )            
FIG. 2 illustrates the conventional peak windowing. The waveform of a baseband signal is shown in the upper part of the drawing, and the scaling factor s(n) for eliminating peaks (|x(k)|) at or above a threshold (=A) is shown in the lower part.
Referring to FIG. 2, the scaling factor s(n) to be multiplied by the amplitude x(n) of the baseband signal is set to ‘1’ when x(n) is less than A. If x(n) is greater than A, an impulse is generated according to the ratio of the amplitude of an input signal at a peak to the threshold and a convolution of the impulse and a predetermined window is subtracted from ‘1’. The resulting signal is set as s(n). The convolution can be implemented by use of a Finite Impulse Response (FIR) filter.
Consequently, the peak windowing technique is expressed as Equation (4):|xs(n)|=s(n)·|x(n)|  (4)
When peaks exceeding the threshold appear at smaller intervals than the window size W, scaling factors are overlapped with each other, as indicated by reference character (a) in FIG. 3. Therefore, the amplitude of the original signal is restricted more than desired. Moreover, the scaling factors become negative values, thereby causing problematic errors to the system. This problem is more or less overcome by inserting a Blocking Negative Value (BNV) and adding feedback to a window of a FIR filter structure.
However, this peak windowing technique using feedback still has the problem of excess limitation of the amplitude of the original signal due to the overlapped scaling factors, when peaks are generated at smaller intervals than a window size. In this case, the average BER of the receiver is increased.
Referring to FIG. 7, in a conventional waveform denoted by AFTER PEAK WINDOWING, when peaks at or above a threshold are created at smaller intervals than a window size, they are controlled so as not to exceed the threshold. However, if peaks at or above the threshold appear successively, their amplitudes are restricted too much. As a result, the average BER of the receiver is increased, as described before.